
\documentclass[tikz,border=10pt]{standalone}


\RequirePackage{luatex85}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amssymb, amsfonts, accents}
\usetikzlibrary{graphdrawing, graphs, arrows, shapes, automata, calc, decorations}
\usegdlibrary{trees, layered}
\usepackage{stix}


\newcommand{\Xund}{\rule{.4em}{.4pt}}


\begin{document}

\def\offs{-0.65in}
\def\widd{1in}
\def\dist{1in}

\begin{tikzpicture}[>=stealth, ->, auto, node distance=\dist]

\tikzstyle{every node}=[draw=none]
\tikzstyle{every state}=[rectangle, rounded corners = 6, minimum size=0.18in, inner sep = 3pt]

\tikzset{style1/.style={draw, rectangle, rounded corners = 11, minimum width = \widd, minimum height = 0.3in, xshift = \offs}}
\tikzset{style2/.style={state, accepting, xshift = \offs}}

%\newcommand \retonfa {re \Xund to \Xund n\!f\!a}
%\newcommand \ntag {neg \Xund tag}
\newcommand \retonfa {F}
\newcommand \ntag {N}


\begin{scope}[xshift=0in, yshift=0in]

\begin{scope}[xshift=0in, yshift=0in]
    \node[draw=none] (a) {$\hphantom{\hspace{1in}}$};
\end{scope}

\begin{scope}[xshift=0in, yshift=0in]
    \node[state, accepting] (a) {$y$};
    \node [label={[label distance=0.1in, below left]270:\large{(a)}}] (a) {};
    \node [label={[label distance=0.1in, below right]270:
    $\retonfa \big( (0, 0, \epsilon), y \big) $}] (a) {};
\end{scope}

\begin{scope}[xshift=0in, yshift=-0.7in]
    \node[state] (a) {$x$};
    \node[state, accepting, right of=a] (b) {$y$};
    \path (a) edge node {$\alpha / \epsilon$} (b);
    \node [label={[label distance=0.1in, below left]270:\large{(b)}}] (a) {};
    \node [label={[label distance=0.1in, below right]270:
    $\retonfa \big( (0, 0, a), y \big) $}] (a) {};
\end{scope}

\begin{scope}[xshift=0in, yshift=-1.4in]
    \def\offs{-0.5in}
    \def\widd{1.3in}

    \node[state] (a1) {$z$};
    \node[style1, right of = a1] (a) {$F(s)$};
    \node[style2, right of = a] (a2) {$x$};
    \node[style1, right of = a2] (b) {$F(u)$};
    \node[style2, right of = b] (b2) {$y$};
    \node [label={[label distance=0.2in, below left]270:\large{(c)}}] (a) {};
    \node [label={[label distance=0.2in, below right]270:
    $\retonfa \big( (0, 0, s \cdot u), y \big) $}] (a1) {};
\end{scope}

\begin{scope}[xshift=0in, yshift=-2.6in]
    \def\offs{-0.5in}
    \def\widd{1.3in}

    \node[state] (a) {$x$};
    \node[state, above right of = a, yshift = -0.35in] (b1) {$x_2$};
    \node[style1, right of = b1] (b) {$F(s)$};
    \node[style2, right of = b] (b2) {$x_1$};
    \node[style1, right of = b2, rotate around={-21:(b2)}] (d) {$N(u)$};

    \node[state, below right of=a, yshift = 0.35in] (c1) {$x_4$};
    \node[style1, right of = c1] (c2) {$N(s)$};
    \node[style2, right of = c2] (c3) {$x_3$};
    \node[style1, right of = c3, rotate around={21:(c3)}] (c) {$F(u)$};
    \node[style2, right of = c, rotate around={21:(c)}] (d) {$y$};
    \path
        (a)  edge [bend left]  node {$1 / \epsilon$} (b1)
        (a)  edge [bend right] node [below left] {$2 / \epsilon $} (c1)
    ;
    \node [label={[label distance=0.5in, below left]270:\large{(d)}}] (a) {};
    \node [label={[label distance=0.5in, below right]270:
    $\retonfa \big( (0, 0, s \mid u), y \big) $}] (a) {};
\end{scope}

\begin{scope}[xshift=0in, yshift=-3.8in]
    \def\offs{-0.5in}
    \def\widd{1.3in}

    \node[state] (a1) {$z$};
    \node[style1, right of = a1] (a) {$F(r)$};
    \node[style2, right of = a] (a2) {$x$};
    \node[style1, right of = a2, minimum width = 1.9in, xshift = 0.3in] (b) {$F( (0, 0, r^{n-1, m-1}))$};
    \node[style2, right of = b, xshift = 0.3in] (b2) {$y$};
    \node [label={[label distance=0.2in, below left]270:\large{(e)}}] (a1) {};
    \node [label={[label distance=0.2in, below right]270:
    $\retonfa \big( (0, 0, r^{n, m}), y \big) \mid_{n \;>\; 1} $}] (a1) {};
\end{scope}

\begin{scope}[xshift=0in, yshift=-5in]
    \def\offs{-0.5in}
    \def\widd{1.3in}

    \node[state] (a) {$x$};
    \node[state, above right of = a, yshift = -0.35in] (b1) {$x_1$};
    \node[style1, right of = b1, rotate around={-21:(b1)}] (d) {$F( (0, 0, r^{1,m}))$};

    \node[state, below right of=a, yshift = 0.35in] (c1) {$x_2$};
    \node[style1, right of = c1, rotate around={21:(c1)}] (c) {$N(r)$};
    \node[style2, right of = c, rotate around={21:(c)}] (d) {$y$};
    \path
        (a)  edge [bend left]  node {$1 / \epsilon$} (b1)
        (a)  edge [bend right] node [below left] {$2 / \epsilon $} (c1)
    ;
    \node [label={[label distance=0.5in, below left]270:\large{(f)}}] (a) {};
    \node [label={[label distance=0.5in, below right]270:
    $\retonfa \big( (0, 0, r^{0, m}), y \big) $}] (a) {};
\end{scope}

\begin{scope}[xshift=0in, yshift=-6.6in]
    \def\offs{-0.5in}
    \def\widd{1.3in}

    \node[state] (b1) {$z$};
    \node[style1, right of = b1] (b) {$F(r)$};
    \node[style2, right of = b] (b2) {$x$};

    \node[state, accepting, right of = b2] (c) {$y$};

    \path
        (b2) edge node {$2 / \epsilon$} (c)
    ;
    \draw (b2) .. controls ($ (b2) + (0.7, 1.5) $) and ($ (b1) + (-0.7, 1.5) $) .. node [above] {$1 / \epsilon$} (b1);
    \node [label={[label distance=0.2in, below left]270:\large{(g)}}] (b1) {};
    \node [label={[label distance=0.2in, below right]270:
    $\retonfa \big( (0, 0, r^{1, \infty}), y \big) $}] (b1) {};
\end{scope}

\begin{scope}[xshift=0in, yshift=-7.4in]
    \def\offs{-0.5in}
    \def\widd{1.3in}

    \node[state] (b1) {$x$};
    \node[style1, right of = b1] (b) {$F(r)$};
    \node[style2, right of = b] (b2) {$y$};

    \node [label={[label distance=0.2in, below left]270:\large{(h)}}] (b1) {};
    \node [label={[label distance=0.2in, below right]270:
    $\retonfa \big( (0, 0, r^{1, 1}), y \big) $}] (b1) {};
\end{scope}

\begin{scope}[xshift=0in, yshift=-8.6in]
    \def\offs{-0.5in}
    \def\widd{1.3in}

    \node[state] (b1) {$w$};
    \node[style1, right of = b1] (b) {$F(r)$};
    \node[style2, right of = b] (b2) {$z$};

    \node[state, right of = b2] (c1) {$x$};
    \node[style1, right of = c1, minimum width = 1.7in, xshift = 0.2in] (c) {$F((0, 0, r^{1, m-1}))$};
    \node[style2, right of = c, xshift = 0.2in] (c2) {$y$};

    \path
        (b2) edge node {$2 / \epsilon$} (c1)
    ;
    \draw (b2) .. controls ($ (b2) + (0, 2) $) and ($ (c2) + (0, 2) $) .. node [very near start] {$1 / \epsilon$} (c2);
    \node [label={[label distance=0.2in, below left]270:\large{(h)}}] (b1) {};
    \node [label={[label distance=0.2in, below right]270:
    $\retonfa \big( (0, 0, r^{1, m}), y \big) \mid_{1 < m < \infty} $}] (b1) {};
\end{scope}

\begin{scope}[xshift=0in, yshift=-10in]
    \def\offs{-0.5in}
    \def\widd{1.3in}

    \node[state] (a) {$w$};
    \node[state, above right of=a, xshift=-0.2in, yshift=-0.2in] (b1) {$z$};
    \node[style1, right of = b1] (b) {$F ( (0, 0, r) )$};
    \node[style2, right of = b] (b2) {$x$};
    \node[state, accepting, below right of=b2, xshift=-0.2in, yshift=0.2in] (d) {$y$};
    \path
        (a) edge node {$1 / 2i \!-\! 1 $} (b1)
        (b2) edge node {$1 / 2i $} (d)
    ;
    \node [label={[label distance=0.1in, below left]270:\large{(i)}}] (a) {};
    \node [label={[label distance=0.1in, below right]270:
    $\retonfa \big( (i, \Xund, r) \big) \mid_{i \;\neq\; 0} $}] (a) {};
\end{scope}

\begin{scope}[xshift=0in, yshift=-10.8in]
    \def\offs{-0.5in}
    \def\widd{1.3in}

    \node[state] (a) {$x_0$};
    \node[state, right of = a] (a1) {$x_1$};
    \node[draw=none, right of = a1, xshift=-0.5in] (b) {\large{$\dots$}};
    \node[state, right of = b, xshift=-0.5in] (b1) {$x_{2n-1}$};
    \node[state, accepting, right of = b1] (b2) {$x_{2n}$};
    \path
        (a) edge node {$1 / 1\!-\!2i $} (a1)
        (a1) edge node {} (b)
        (b) edge node {} (b1)
        (b1) edge node {$1 / -\! 2i $} (b2)
    ;
    \node [label={[label distance=0.1in, below left]270:\large{(j)}}] (a) {};
    \node [label={[label distance=0.1in, below right]270:
    $\begin{aligned}
        N \big( (i, \Xund, r) \big)
    \end{aligned}$
    }] (a) {};
\end{scope}

\end{scope}


\end{tikzpicture}



\end{document}

